Tractography from the software phantom without noise (a), from the phantom with overlaid noise (b) and from the noisy, regularized phantom (c) demonstrating the improvement of fiber homogeneity due to regularization.

<p>Tractography from the software phantom without noise (a), from the phantom with overlaid noise (b) and from the noisy, regularized phantom (c) demonstrating the improvement of fiber homogeneity due to regularization.</p

Twelve independent components obtained by means of ICA from 12

<p>The components IC₁–IC₆ (upper row) contain information about tissue microstructure and directed diffusion, the components IC₇–IC₁₂ (lower row) contain noise information. Images are scaled equally and displayed in inverted view.</p

and .show the standard deviation of the noise for two of six noise tensor elements and that serve as input for Eq. [13].

<p>The spatially varying regularization parameter was updated at each iteration step. This is shown for two regions of interest (ROI 1, ROI 2) for the regularization tensor elements and .</p

Evaluated tractography parameters Mean Length (ML), Track Count (TC), Volume (V), and Voxel Count (VC) for the noise-free phantom, the phantom with overlaid noise from ten measurements (mean ± standard deviation) and the noisy phantom with regularization (mean ± standard deviation).

<p>Evaluated tractography parameters Mean Length (ML), Track Count (TC), Volume (V), and Voxel Count (VC) for the noise-free phantom, the phantom with overlaid noise from ten measurements (mean ± standard deviation) and the noisy phantom with regularization (mean ± standard deviation).</p

FA map from data obtained using one measurement (first out of three averages) (a), FA map from the denoised set of DWI data () (b) showing only marginal differences compared with (a), FA map from data obtained using three averages (c), FA map from data obtained using one measurement (first out of three averages) with regularization (first row) (d).

<p>The second row shows magnified views from the region marked in the first image.</p

Diffusion tensor elements for one average (first row) and for one average regularized (second row).

<p>Rows three and four show a magnified view from the region marked in the first image.</p

Evaluation of tractography parameters Mean Length, Track Count, Volume and Voxel Count for rs-EPI data obtained from one average (rs-EPI₁), two averages (rs-EPI₂), three averages (rs-EPI₃) and from one average processed with the regularization algorithm (rs-EPI_1,reg) for the entire brain for both subjects.

<p>Please note that errorbars in rs-EPI_1, rs-EPI₂ and rs-EPI_1,reg denote the standard deviation due to the separate evaluation of all three measurements and their combination respectively.</p

Schematic overview of the adaptive spatially varying regularization algorithm.

<p> denotes the diffusion-weighted images, IC the independent components decomposed by ICA, are the denoised diffusion-weighted images with the corresponding noise images is the diffusion tensor with the corresponding noise tensor , evaluated using the Stejskal-Tanner equation (ST). The noise variance tensor was estimated by averaging the variance in a 5×5 pixel moving window (SD). denotes the regularization tensor to estimate the sought regularized diffusion tensor .</p

Comparison of FA maps from conventional ss-EPI data (a) with a resolution of 2.5×2.5×2.5 mm³ with high resolution rs-EPI data (b) with a resolution of 1×1×2.5 mm³.

<p>Small structures such as the fornix (marked by the arrow) or branches in peripheral regions can hardly be seen in conventional DTI scans with limited resolution but can be clearly identified in high resolution rs-EPI.</p

Descriptive statistics and scores of neuropsychological and clinical testing for MS patients; means and standard deviations (in brackets).

<p>Legend: N  =  sample size; EDSS  =  expanded disability status scale; SRT  =  selective reminding test; SPAT  =  spatial recall test; PASAT  =  paced auditory serial addition test; SDMT  =  symbol digit modalities test; WLG  =  word list generation; CIS  =  clinically isolated syndrome; RRMS  =  relapsing remitting MS; SPMS  =  secondary progressive MS; f  =  female; m  =  male.</p